1. Exercise Write in fraction form: 2 : 7 as 6 : 21. 2727 2727 6 21 = = What are the extremes? 2; 21 What are the means? 7; 6 Does the product of the extremes equal the product of the means? What is the product? yes; 42

2. 2323 2323 Use the rule for dividing rational numbers to find the quotient. 50 2323 2323 × × 1 50 1 75 = = Exercise

3. The scale for a drawing or map is the ratio of the drawing’s length to the actual length. Scale

4. A scale drawing is a drawing in which all of the lengths are at the same scale, or ratio, to the actual lengths of the object. Scale Drawing

5. A scale is a ratio. 1 in. 10 ft. 1 in. 120 in. == 1 120 == of actual size

6. Find the length of a bridge in a drawing if the scale is 1 cm : 5 m and the actual length is 27 m. Let b = the length of the bridge in the drawing. 1515 1515 == b 27 5b = 27 5555 b = 5.4 cm Example 1

7. The distance between two towns on a map is 3.6 cm. The scale on the map is 2 cm : 15 km. What is the actual distance between the towns? Let n = the actual distance between the two towns. Example 2

8. The distance between two towns on a map is 3.6 cm. The scale on the map is 2 cm : 15 km. What is the actual distance between the towns? 2 15 == 3.6 n 2n = 54 2222 n = 27 km

9. Find the distance from Carville to Danville. Carville Danville 5 cm scale – 2 cm : 25 km 2 25 == 5n5n 5n5n 2n = 125 2222 n = 62.5 km Example 3

10. If a model airplane is constructed on a 1 in. : 25 ft. scale, what is the actual length of the airplane if the length of the model is 9 in.? 225 ft. Example

11. If a map is drawn on a 1 in. : 50 mi. scale, what is the distance between towns if the distance on the map is 2.5 in.? 125 mi. Example

12. How far apart on a map with a scale of 1 in. : 50 mi. should two towns be drawn if they are actually 275 mi. apart? 5.5 in. Example

13. A map is to be made with a scale of 1 in. to 40 mi. How far apart will two cities appear on the map if they are actually 55 mi. from each other? Let n = the map distance. 1 40 == n 55 40n = 55 40 n = 1 in. 3838 3838 Example 4

14. Find the scale used if two cities that are 60 mi. apart appear on a map in. apart. 3434 3434 60 mi. 3434 3434 ÷ 60 3434 3434 xx 3434 3434 == 1 60 1 1 20 1 80 = = Example 5 The scale is 1 in. : 80 mi.

15. If the circumference of the earth is about 25,000 mi., what should be the scale of a globe if it is to have a circumference of 2.5 ft.? 30 in. : 25,000 mi. 1 in. : 833.33 mi. Example

16. If that same globe has relief (e.g. it is raised where there are mountains), then how high should Mt. Everest be raised on the globe if it is 29,000 ft. high? 0.006 in. Example

17. A blueprint of a house is drawn to a scale of 1 in. : 5 ft. If a bedroom is 10 ft. by 12 ft., what are its dimensions on the blueprint? 2 in. by 2.4 in. Example

18. In the science classroom, which measures 20 ft. by 20 ft., the teacher wishes to hang a scale model of the solar system from the ceiling. She plans to hang the sun in the center of the room and Neptune, which is 2.8 billion mi. from the sun, in a corner 14 ft. away. Determine the scale of the model. 1 ft : 0.2 billion mi. Example

19. How far from the center of the room should Earth be placed if it is about 93 million mi. from the sun? 0.465 ft. Example

20. If a 2.5 in. x 3.5 in. photo is to be enlarged to 5 in. x 7 in., what enlargement setting would be used? Let p = the % enlargement. 2.5p = 5 200% enlargement 2.5 p = 2 Example 6

21. A 10 cm x 16 cm table of data is reduced using a copier setting of 67%. What are the dimensions of the new table? 10(0.67) 6.7 cm x 10.7 cm = 6.7 cm 16(0.67) = 10.7 cm Example 7

22. If a picture in a book is labeled and an object in the photo is 5 in. wide, how wide is the real object? 30 x 5 in. = 12.5 ft. wide = 150 in. 1 30 150 12 ft. Example 8

23. Find the size of a 3 in. by 5 in. photo if it is enlarged 250%. 7.5 in. by 12.5 in. Example

24. What should the enlargement of a 3 in. by 4 in. photograph be if you wish to place in on 9 in. by 12 in. paper? 300% Example